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   "source": [
    "# Estimating The Infected Population From Deaths\n",
    "> Estimating the number of infected people by country based on the number of deaths and case fatality rate. \n",
    "\n",
    "- comments: true\n",
    "- author: Joao B. Duarte\n",
    "- categories: [growth, compare, interactive, estimation]\n",
    "- hide: false\n",
    "- image: images/covid-estimate-infections.png\n",
    "- permalink: /covid-infected/\n",
    "- toc: true"
   ]
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   "source": [
    "> Warning: This analysis contains the results of a predictive model. There are a number of assumptions made which include some speculation.  Furthermore, this analysis was not prepared or reviewed by an Epidimiologist. Therefore, the assumptions and methods presented should be scrutinized carefully before arriving at any conclusions. "
   ]
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   "source": [
    "#hide\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import altair as alt\n",
    "from datetime import timedelta, datetime, date\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "chart_width = 550\n",
    "chart_height= 400"
   ]
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   "source": [
    "#hide\n",
    "def plot(data, type1, levels):\n",
    "    data_countries_pc2 = data.copy()\n",
    "    for i in range(0,len(countries)):\n",
    "        data_countries_pc2[i] = data_countries_pc2[i].reset_index()\n",
    "        data_countries_pc2[i]['n_days'] = data_countries_pc2[i].index\n",
    "        if type1 == \"scatter\":\n",
    "            data_countries_pc2[i]['cases'] = data_countries_pc2[i][\"total_cases\"]\n",
    "        data_countries_pc2[i]['infected'] = data_countries_pc2[i][\"total_infected\"]\n",
    "    data_plot = data_countries_pc2[0]\n",
    "    for i in range(1, len(countries)):    \n",
    "        data_plot = pd.concat([data_plot, data_countries_pc2[i]], axis=0)\n",
    "    \n",
    "    if type1 == \"scatter\":\n",
    "        data_plot[\"45_line\"] = data_plot[\"cases\"]\n",
    "\n",
    "    # Plot it using Altair\n",
    "    source = data_plot\n",
    "    \n",
    "    if levels == True:\n",
    "        ylabel = \"Total\"\n",
    "    else :\n",
    "        ylabel = \"Per Million\"\n",
    "\n",
    "    scales = alt.selection_interval(bind='scales')\n",
    "    selection = alt.selection_multi(fields=['location'], bind='legend')\n",
    "\n",
    "    if type1 == \"line\": \n",
    "        base = alt.Chart(source, title =  \"Estimated Infected Population By Country\").encode(\n",
    "            x = alt.X('n_days:Q', title = \"Days since outbreak\"),\n",
    "            y = alt.Y(\"infected:Q\",title = ylabel),\n",
    "            color = alt.Color('location:N', legend=alt.Legend(title=\"Country\", labelFontSize=15, titleFontSize=17),\n",
    "                             scale=alt.Scale(scheme='tableau20'))\n",
    "        )\n",
    "        \n",
    "        shades = base.mark_area().encode(\n",
    "            x='n_days:Q',\n",
    "            y='total_infected_lower:Q',\n",
    "            y2='total_infected_upper:Q',\n",
    "            opacity = alt.condition(selection, alt.value(0.2), alt.value(0.05))\n",
    "        )\n",
    "    \n",
    "        lines = base.mark_line().encode(\n",
    "            opacity = alt.condition(selection, alt.value(1), alt.value(0.1))\n",
    "        ).add_selection(\n",
    "            scales\n",
    "        ).add_selection(\n",
    "            selection\n",
    "        ).properties(\n",
    "            width=chart_width,\n",
    "            height=chart_height\n",
    "        )\n",
    "        return(\n",
    "        ( lines + shades)\n",
    "        .configure_title(fontSize=20)\n",
    "        .configure_axis(labelFontSize=15,titleFontSize=18)\n",
    "        )\n",
    "    \n",
    "    if levels == True:\n",
    "        ylabel = \"Infected\"\n",
    "        xlabel = \"Cases\"\n",
    "    else :\n",
    "        ylabel = \"Per Million Infected\"\n",
    "        xlabel = \"Per Million Cases\"\n",
    "        \n",
    "    if type1 == \"scatter\":\n",
    "        base = alt.Chart(source, title = \"COVID-19 Cases VS Infected\").encode(\n",
    "            x = alt.X('cases:Q', title = xlabel),\n",
    "            y = alt.Y(\"infected:Q\",title = ylabel),\n",
    "            color = alt.Color('location:N', legend=alt.Legend(title=\"Country\", labelFontSize=15, titleFontSize=17),\n",
    "                             scale=alt.Scale(scheme='tableau20')),\n",
    "            opacity = alt.condition(selection, alt.value(1), alt.value(0.1))\n",
    "        )\n",
    "\n",
    "        \n",
    "        scatter = base.mark_point().add_selection(\n",
    "            scales\n",
    "        ).add_selection(\n",
    "            selection\n",
    "        ).properties(\n",
    "            width=chart_width,\n",
    "            height=chart_height\n",
    "        )\n",
    "\n",
    "        line_45 = alt.Chart(source).encode(\n",
    "            x = \"cases:Q\",\n",
    "            y = alt.Y(\"45_line:Q\",  scale=alt.Scale(domain=(0, max(data_plot[\"infected\"])))),\n",
    "        ).mark_line(color=\"grey\", strokeDash=[3,3])\n",
    "        \n",
    "        return(\n",
    "        (scatter + line_45)\n",
    "        .configure_title(fontSize=20)\n",
    "        .configure_axis(labelFontSize=15,titleFontSize=18)\n",
    "        )"
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      "/opt/hostedtoolcache/Python/3.6.10/x64/lib/python3.6/site-packages/ipykernel_launcher.py:47: RuntimeWarning: invalid value encountered in true_divide\n"
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      "/opt/hostedtoolcache/Python/3.6.10/x64/lib/python3.6/site-packages/ipykernel_launcher.py:68: RuntimeWarning: invalid value encountered in true_divide\n"
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      "/opt/hostedtoolcache/Python/3.6.10/x64/lib/python3.6/site-packages/ipykernel_launcher.py:84: RuntimeWarning: invalid value encountered in true_divide\n"
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   "source": [
    "#hide \n",
    "# Get data on deaths D_t\n",
    "data = pd.read_csv(\"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv\", \n",
    "                   error_bad_lines=False)\n",
    "data = data.drop(columns=[\"Lat\", \"Long\"])\n",
    "data = data.melt(id_vars= [\"Province/State\", \"Country/Region\"])\n",
    "data = pd.DataFrame(data.groupby(['Country/Region', \"variable\"]).sum())\n",
    "data.reset_index(inplace=True)  \n",
    "data = data.rename(columns={\"Country/Region\": \"location\", \"variable\": \"date\", \"value\": \"total_deaths\"})\n",
    "data['date'] =pd.to_datetime(data.date)\n",
    "data = data.sort_values(by = \"date\")\n",
    "data.loc[data.location == \"US\",\"location\"] = \"United States\"\n",
    "data.loc[data.location == \"Korea, South\",\"location\"] = \"South Korea\"\n",
    "\n",
    "#hide\n",
    "# Get data and clean it\n",
    "data_cases = pd.read_csv(\"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv\", error_bad_lines=False)\n",
    "\n",
    "data_cases = data_cases.drop(columns=[\"Lat\", \"Long\"])\n",
    "data_cases = data_cases.melt(id_vars= [\"Province/State\", \"Country/Region\"])\n",
    "data_cases = pd.DataFrame(data_cases.groupby(['Country/Region', \"variable\"]).sum())\n",
    "data_cases.reset_index(inplace=True)  \n",
    "data_cases = data_cases.rename(columns={\"Country/Region\": \"location\", \"variable\": \"date\", \"value\": \"total_cases\"})\n",
    "data_cases['date'] =pd.to_datetime(data_cases.date)\n",
    "data_cases = data_cases.sort_values(by = \"date\")\n",
    "data_cases.loc[data_cases.location == \"US\",\"location\"] = \"United States\"\n",
    "data_cases.loc[data_cases.location == \"Korea, South\",\"location\"] = \"South Korea\"\n",
    "# Add countries\n",
    "countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
    "             \"Portugal\", \"United States\", \"Singapore\",\"South Korea\", \"Japan\", \n",
    "             \"Brazil\",\"Iran\", \"India\", \"Switzerland\", \"Canada\", \"Australia\", \n",
    "             \"Russia\", \"Belarus\", \"Ukraine\"]\n",
    "\n",
    "data_final = pd.merge(data,\n",
    "                 data_cases\n",
    "                 )\n",
    "data_final[\"CFR\"] = data_final[\"total_deaths\"]/data_final[\"total_cases\"]\n",
    "\n",
    "\n",
    "data_final[\"total_infected\"] = np.NaN\n",
    "data_final = data_final.sort_values(by = ['location', 'date'])\n",
    "data_final = data_final.reset_index(drop = True)\n",
    "\n",
    "\n",
    "for j in countries:\n",
    "    for i in data_final[\"date\"].unique()[0:-8]:\n",
    "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]\n",
    "        \n",
    "\n",
    "# Estimate growth rate of infected, g        \n",
    "data_final['infected_g'] = np.log(data_final['total_infected'])\n",
    "data_final['infected_g'] = data_final['infected_g'].diff() \n",
    "\n",
    "# Estimate number of infected given g\n",
    "today = data_final.date.iloc[-1]\n",
    "for j in countries:\n",
    "    for i in range(7,-1,-1):\n",
    "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected\"] = data_final.loc[data_final.location == j, \"total_infected\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
    "    \n",
    "\n",
    "\n",
    "# Upper Bound\n",
    "data_final[\"total_infected_upper\"] = np.NaN\n",
    "data_final = data_final.sort_values(by = ['location', 'date'])\n",
    "data_final = data_final.reset_index(drop = True)\n",
    "for j in countries:\n",
    "    for i in data_final[\"date\"].unique()[0:-8]:\n",
    "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected_upper\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/(data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]*0.7)\n",
    "# Estimate growth rate of infected, g        \n",
    "data_final['infected_g'] = np.log(data_final['total_infected_upper'])\n",
    "data_final['infected_g'] = data_final['infected_g'].diff() \n",
    "# Estimate number of infected given g \n",
    "today = data_final.date.iloc[-1]\n",
    "for j in countries:\n",
    "    for i in range(7,-1,-1):\n",
    "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected_upper\"] = data_final.loc[data_final.location == j, \"total_infected_upper\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
    "\n",
    "# Lower Bound\n",
    "data_final[\"total_infected_lower\"] = np.NaN\n",
    "data_final = data_final.sort_values(by = ['location', 'date'])\n",
    "data_final = data_final.reset_index(drop = True)\n",
    "for j in countries:\n",
    "    for i in data_final[\"date\"].unique()[0:-8]:\n",
    "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected_lower\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/(data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]*1.3)\n",
    "# Estimate growth rate of infected, g        \n",
    "data_final['infected_g'] = np.log(data_final['total_infected_lower'])\n",
    "data_final['infected_g'] = data_final['infected_g'].diff() \n",
    "# Estimate number of infected given g \n",
    "today = data_final.date.iloc[-1]\n",
    "for j in countries:\n",
    "    for i in range(7,-1,-1):\n",
    "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected_lower\"] = data_final.loc[data_final.location == j, \"total_infected_lower\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
    "data_final.loc[data_final.total_infected_lower < data_final.total_cases, \"total_infected_lower\"] = data_final.loc[data_final.total_infected_lower < data_final.total_cases, \"total_cases\"]\n",
    "\n",
    "\n",
    "data_pc = data_final[['location', 'date', 'total_infected', 'total_infected_lower', 'total_infected_upper']].copy()\n",
    "\n",
    "countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
    "             \"Portugal\", \"United States\", \"Singapore\",\"South Korea\", \"Japan\", \n",
    "             \"Brazil\",\"Iran\"]\n",
    "data_countries = []\n",
    "data_countries_pc = []\n",
    "\n",
    "for i in countries:\n",
    "    data_pc.loc[data_pc.location == i,\"total_infected\"] = data_pc.loc[data_pc.location == i,\"total_infected\"]\n",
    "\n",
    "# Get each country time series\n",
    "filter1 = data_pc[\"total_infected\"] > 1\n",
    "for i in countries:\n",
    "    filter_country = data_pc[\"location\"]== i\n",
    "    data_countries_pc.append(data_pc[filter_country & filter1])      "
   ]
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   "source": [
    "## Estimated Infected Population By Country\n",
    "\n",
    "with respect to days since outbreak\n",
    "\n",
    "> Tip: Click (Shift+ for multiple) on countries in the legend to filter the visualization. "
   ]
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\"total_infected\": 388.0, \"total_infected_lower\": 298.46153846153845, \"total_infected_upper\": 554.2857142857143, \"n_days\": 9, \"infected\": 388.0}, {\"index\": 6350, \"location\": \"Iran\", \"date\": \"2020-02-21T00:00:00\", \"total_infected\": 593.0, \"total_infected_lower\": 456.15384615384613, \"total_infected_upper\": 847.1428571428571, \"n_days\": 10, \"infected\": 593.0}, {\"index\": 6351, \"location\": \"Iran\", \"date\": \"2020-02-22T00:00:00\", \"total_infected\": 978.0, \"total_infected_lower\": 752.3076923076923, \"total_infected_upper\": 1397.142857142857, \"n_days\": 11, \"infected\": 978.0}, {\"index\": 6352, \"location\": \"Iran\", \"date\": \"2020-02-23T00:00:00\", \"total_infected\": 1501.0, \"total_infected_lower\": 1154.6153846153845, \"total_infected_upper\": 2144.285714285714, \"n_days\": 12, \"infected\": 1501.0}, {\"index\": 6353, \"location\": \"Iran\", \"date\": \"2020-02-24T00:00:00\", \"total_infected\": 2336.0, \"total_infected_lower\": 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\"total_infected_upper\": 8318.571428571428, \"n_days\": 17, \"infected\": 5823.0}, {\"index\": 6358, \"location\": \"Iran\", \"date\": \"2020-02-29T00:00:00\", \"total_infected\": 6566.0, \"total_infected_lower\": 5050.7692307692305, \"total_infected_upper\": 9380.0, \"n_days\": 18, \"infected\": 6566.0}, {\"index\": 6359, \"location\": \"Iran\", \"date\": \"2020-03-01T00:00:00\", \"total_infected\": 7161.000000000001, \"total_infected_lower\": 5508.461538461539, \"total_infected_upper\": 10230.000000000002, \"n_days\": 19, \"infected\": 7161.000000000001}, {\"index\": 6360, \"location\": \"Iran\", \"date\": \"2020-03-02T00:00:00\", \"total_infected\": 8042.000000000001, \"total_infected_lower\": 6186.153846153847, \"total_infected_upper\": 11488.57142857143, \"n_days\": 20, \"infected\": 8042.000000000001}, {\"index\": 6361, \"location\": \"Iran\", \"date\": \"2020-03-03T00:00:00\", \"total_infected\": 9000.0, \"total_infected_lower\": 6923.076923076924, \"total_infected_upper\": 12857.142857142859, \"n_days\": 21, \"infected\": 9000.0}, {\"index\": 6362, \"location\": \"Iran\", \"date\": \"2020-03-04T00:00:00\", \"total_infected\": 10075.0, \"total_infected_lower\": 7750.0, \"total_infected_upper\": 14392.857142857145, \"n_days\": 22, \"infected\": 10075.0}, {\"index\": 6363, \"location\": \"Iran\", \"date\": \"2020-03-05T00:00:00\", \"total_infected\": 11364.0, \"total_infected_lower\": 8741.538461538461, \"total_infected_upper\": 16234.285714285714, \"n_days\": 23, \"infected\": 11364.0}, {\"index\": 6364, \"location\": \"Iran\", \"date\": \"2020-03-06T00:00:00\", \"total_infected\": 12729.0, \"total_infected_lower\": 9791.538461538461, \"total_infected_upper\": 18184.285714285714, \"n_days\": 24, \"infected\": 12729.0}, {\"index\": 6365, \"location\": \"Iran\", \"date\": \"2020-03-07T00:00:00\", \"total_infected\": 13938.0, \"total_infected_lower\": 10721.538461538463, \"total_infected_upper\": 19911.428571428572, \"n_days\": 25, \"infected\": 13938.0}, {\"index\": 6366, \"location\": \"Iran\", \"date\": \"2020-03-08T00:00:00\", \"total_infected\": 14991.0, \"total_infected_lower\": 11531.538461538461, \"total_infected_upper\": 21415.714285714286, \"n_days\": 26, \"infected\": 14991.0}, {\"index\": 6367, \"location\": \"Iran\", \"date\": \"2020-03-09T00:00:00\", \"total_infected\": 16169.0, \"total_infected_lower\": 12437.692307692307, \"total_infected_upper\": 23098.57142857143, \"n_days\": 27, \"infected\": 16169.0}, {\"index\": 6368, \"location\": \"Iran\", \"date\": \"2020-03-10T00:00:00\", \"total_infected\": 17361.0, \"total_infected_lower\": 13354.615384615383, \"total_infected_upper\": 24801.428571428572, \"n_days\": 28, \"infected\": 17361.0}, {\"index\": 6369, \"location\": \"Iran\", \"date\": \"2020-03-11T00:00:00\", \"total_infected\": 18407.0, \"total_infected_lower\": 14159.230769230768, \"total_infected_upper\": 26295.714285714283, \"n_days\": 29, \"infected\": 18407.0}, {\"index\": 6370, \"location\": \"Iran\", \"date\": \"2020-03-12T00:00:00\", \"total_infected\": 19644.0, \"total_infected_lower\": 15110.76923076923, \"total_infected_upper\": 28062.85714285715, \"n_days\": 30, \"infected\": 19644.0}, {\"index\": 6371, \"location\": \"Iran\", \"date\": \"2020-03-13T00:00:00\", \"total_infected\": 20610.0, \"total_infected_lower\": 15853.846153846152, \"total_infected_upper\": 29442.857142857145, \"n_days\": 31, \"infected\": 20610.0}, {\"index\": 6372, \"location\": \"Iran\", \"date\": \"2020-03-14T00:00:00\", \"total_infected\": 21638.0, \"total_infected_lower\": 16644.615384615387, \"total_infected_upper\": 30911.428571428576, \"n_days\": 32, \"infected\": 21638.0}, {\"index\": 6373, \"location\": \"Iran\", \"date\": \"2020-03-15T00:00:00\", \"total_infected\": 23049.0, \"total_infected_lower\": 17730.0, \"total_infected_upper\": 32927.142857142855, \"n_days\": 33, \"infected\": 23049.0}, {\"index\": 6374, \"location\": \"Iran\", \"date\": \"2020-03-16T00:00:00\", \"total_infected\": 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27236.923076923074, \"total_infected_upper\": 50582.857142857145, \"n_days\": 38, \"infected\": 35408.0}, {\"index\": 6379, \"location\": \"Iran\", \"date\": \"2020-03-21T00:00:00\", \"total_infected\": 38309.0, \"total_infected_lower\": 29468.461538461535, \"total_infected_upper\": 54727.14285714286, \"n_days\": 39, \"infected\": 38309.0}, {\"index\": 6380, \"location\": \"Iran\", \"date\": \"2020-03-22T00:00:00\", \"total_infected\": 41495.0, \"total_infected_lower\": 31919.23076923077, \"total_infected_upper\": 59278.571428571435, \"n_days\": 40, \"infected\": 41495.0}, {\"index\": 6381, \"location\": \"Iran\", \"date\": \"2020-03-23T00:00:00\", \"total_infected\": 44604.99999999999, \"total_infected_lower\": 34311.538461538454, \"total_infected_upper\": 63721.42857142857, \"n_days\": 41, \"infected\": 44604.99999999999}, {\"index\": 6382, \"location\": \"Iran\", \"date\": \"2020-03-24T00:00:00\", \"total_infected\": 47593.0, \"total_infected_lower\": 36609.99999999999, \"total_infected_upper\": 67990.0, \"n_days\": 42, \"infected\": 47593.0}, {\"index\": 6383, \"location\": \"Iran\", \"date\": \"2020-03-25T00:00:00\", \"total_infected\": 50467.99999999999, \"total_infected_lower\": 38821.538461538454, \"total_infected_upper\": 72097.14285714286, \"n_days\": 43, \"infected\": 50467.99999999999}, {\"index\": 6384, \"location\": \"Iran\", \"date\": \"2020-03-26T00:00:00\", \"total_infected\": 53183.0, \"total_infected_lower\": 40909.99999999999, \"total_infected_upper\": 75975.71428571429, \"n_days\": 44, \"infected\": 53183.0}, {\"index\": 6385, \"location\": \"Iran\", \"date\": \"2020-03-27T00:00:00\", \"total_infected\": 55743.0, \"total_infected_lower\": 42879.230769230766, \"total_infected_upper\": 79632.85714285714, \"n_days\": 45, \"infected\": 55743.0}, {\"index\": 6386, \"location\": \"Iran\", \"date\": \"2020-03-28T00:00:00\", \"total_infected\": 58226.0, \"total_infected_lower\": 44789.230769230766, \"total_infected_upper\": 83180.0, \"n_days\": 46, \"infected\": 58226.0}, {\"index\": 6387, \"location\": \"Iran\", \"date\": \"2020-03-29T00:00:00\", \"total_infected\": 60500.0, \"total_infected_lower\": 46538.46153846154, \"total_infected_upper\": 86428.57142857143, \"n_days\": 47, \"infected\": 60500.0}, {\"index\": 6388, \"location\": \"Iran\", \"date\": \"2020-03-30T00:00:00\", \"total_infected\": 62589.0, \"total_infected_lower\": 48145.38461538461, \"total_infected_upper\": 89412.85714285714, \"n_days\": 48, \"infected\": 62589.0}, {\"index\": 6389, \"location\": \"Iran\", \"date\": \"2020-03-31T00:00:00\", \"total_infected\": 64586.0, \"total_infected_lower\": 49681.53846153846, \"total_infected_upper\": 92265.7142857143, \"n_days\": 49, \"infected\": 64586.0}, {\"index\": 6390, \"location\": \"Iran\", \"date\": \"2020-04-01T00:00:00\", \"total_infected\": 66220.0, \"total_infected_lower\": 50938.46153846154, \"total_infected_upper\": 94600.00000000001, \"n_days\": 50, \"infected\": 66220.0}, {\"index\": 6391, \"location\": \"Iran\", \"date\": \"2020-04-02T00:00:00\", \"total_infected\": 68349.80971855647, \"total_infected_lower\": 52576.77670658192, \"total_infected_upper\": 97642.58531222354, \"n_days\": 51, \"infected\": 68349.80971855647}, {\"index\": 6392, \"location\": \"Iran\", \"date\": \"2020-04-03T00:00:00\", \"total_infected\": 70548.11973063843, \"total_infected_lower\": 54267.78440818345, \"total_infected_upper\": 100783.02818662634, \"n_days\": 52, \"infected\": 70548.11973063843}, {\"index\": 6393, \"location\": \"Iran\", \"date\": \"2020-04-04T00:00:00\", \"total_infected\": 72817.13318621377, \"total_infected_lower\": 56013.17937401066, \"total_infected_upper\": 104024.4759803054, \"n_days\": 53, \"infected\": 72817.13318621377}, {\"index\": 6394, \"location\": \"Iran\", \"date\": \"2020-04-05T00:00:00\", \"total_infected\": 75159.12409435963, \"total_infected_lower\": 58226.0, \"total_infected_upper\": 107370.17727765664, \"n_days\": 54, \"infected\": 75159.12409435963}, {\"index\": 6395, \"location\": \"Iran\", \"date\": \"2020-04-06T00:00:00\", \"total_infected\": 77576.43960227807, \"total_infected_lower\": 60500.0, \"total_infected_upper\": 110823.48514611155, \"n_days\": 55, \"infected\": 77576.43960227807}, {\"index\": 6396, \"location\": \"Iran\", \"date\": \"2020-04-07T00:00:00\", \"total_infected\": 80071.50234761092, \"total_infected_lower\": 62589.0, \"total_infected_upper\": 114387.86049658703, \"n_days\": 56, \"infected\": 80071.50234761092}, {\"index\": 6397, \"location\": \"Iran\", \"date\": \"2020-04-08T00:00:00\", \"total_infected\": 82646.81288641127, \"total_infected_lower\": 64586.0, \"total_infected_upper\": 118066.8755520161, \"n_days\": 57, \"infected\": 82646.81288641127}, {\"index\": 6398, \"location\": \"Iran\", \"date\": \"2020-04-09T00:00:00\", \"total_infected\": 85304.95219920494, \"total_infected_lower\": 66220.0, \"total_infected_upper\": 121864.21742743564, \"n_days\": 58, \"infected\": 85304.95219920494}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hide_input\n",
    "# Plot estimated absolute number of infected\n",
    "plot1 = plot(data_countries_pc, \"line\", True)\n",
    "plot1.save(\"../images/covid-estimate-infections.png\")\n",
    "plot1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.014929,
     "end_time": "2020-04-10T00:18:57.222026",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.207097",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Latest Country Estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-04-10T00:18:57.279669Z",
     "iopub.status.busy": "2020-04-10T00:18:57.264657Z",
     "iopub.status.idle": "2020-04-10T00:18:57.290101Z",
     "shell.execute_reply": "2020-04-10T00:18:57.289586Z"
    },
    "papermill": {
     "duration": 0.053098,
     "end_time": "2020-04-10T00:18:57.290207",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.237109",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Estimated Infected</th>\n",
       "      <th>Lower Bound Estimates</th>\n",
       "      <th>Upper Bound Estimates</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Brazil</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>45,263</td>\n",
       "      <td>34,818</td>\n",
       "      <td>64,662</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>China</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>83,448</td>\n",
       "      <td>82,883</td>\n",
       "      <td>119,211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>188,038</td>\n",
       "      <td>144,645</td>\n",
       "      <td>268,626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>163,557</td>\n",
       "      <td>125,813</td>\n",
       "      <td>233,653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iran</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>85,305</td>\n",
       "      <td>66,220</td>\n",
       "      <td>121,864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>177,677</td>\n",
       "      <td>143,626</td>\n",
       "      <td>253,824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Japan</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>9,943</td>\n",
       "      <td>7,648</td>\n",
       "      <td>14,204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Portugal</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>21,138</td>\n",
       "      <td>16,260</td>\n",
       "      <td>30,197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Singapore</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>3,932</td>\n",
       "      <td>3,025</td>\n",
       "      <td>5,617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Korea</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>10,804</td>\n",
       "      <td>10,423</td>\n",
       "      <td>15,435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>206,399</td>\n",
       "      <td>158,769</td>\n",
       "      <td>294,856</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United Kingdom</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>119,124</td>\n",
       "      <td>91,634</td>\n",
       "      <td>170,177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United States</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>844,721</td>\n",
       "      <td>649,785</td>\n",
       "      <td>1,206,744</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Date Estimated Infected Lower Bound Estimates  \\\n",
       "Country                                                              \n",
       "Brazil         2020-04-09             45,263                34,818   \n",
       "China          2020-04-09             83,448                82,883   \n",
       "France         2020-04-09            188,038               144,645   \n",
       "Germany        2020-04-09            163,557               125,813   \n",
       "Iran           2020-04-09             85,305                66,220   \n",
       "Italy          2020-04-09            177,677               143,626   \n",
       "Japan          2020-04-09              9,943                 7,648   \n",
       "Portugal       2020-04-09             21,138                16,260   \n",
       "Singapore      2020-04-09              3,932                 3,025   \n",
       "South Korea    2020-04-09             10,804                10,423   \n",
       "Spain          2020-04-09            206,399               158,769   \n",
       "United Kingdom 2020-04-09            119,124                91,634   \n",
       "United States  2020-04-09            844,721               649,785   \n",
       "\n",
       "               Upper Bound Estimates  \n",
       "Country                               \n",
       "Brazil                        64,662  \n",
       "China                        119,211  \n",
       "France                       268,626  \n",
       "Germany                      233,653  \n",
       "Iran                         121,864  \n",
       "Italy                        253,824  \n",
       "Japan                         14,204  \n",
       "Portugal                      30,197  \n",
       "Singapore                      5,617  \n",
       "South Korea                   15,435  \n",
       "Spain                        294,856  \n",
       "United Kingdom               170,177  \n",
       "United States              1,206,744  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hide_input    \n",
    "label = 'Estimated Infected'\n",
    "temp = pd.concat([x.copy() for x in data_countries_pc]).loc[lambda x: x.date >= '3/1/2020']\n",
    "\n",
    "metric_name = f'{label}'\n",
    "temp.columns = ['Country', 'Date', metric_name, \"Lower Bound Estimates\", \"Upper Bound Estimates\"]\n",
    "temp.loc[:, \"Estimated Infected\"] = temp.loc[:, \"Estimated Infected\"].round(0).map('{:,.0f}'.format) \n",
    "temp.loc[:, \"Lower Bound Estimates\"] = temp.loc[:, \"Lower Bound Estimates\"].round(0).map('{:,.0f}'.format) \n",
    "temp.loc[:, \"Upper Bound Estimates\"] = temp.loc[:, \"Upper Bound Estimates\"].round(0).map('{:,.0f}'.format) \n",
    "temp.groupby('Country').last()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.014921,
     "end_time": "2020-04-10T00:18:57.320465",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.305544",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Infected vs. number of confirmed cases\n",
    "> Allows you to compare how countries have been tracking the true number of infected people. The smaller deviation from the dashed line (45 degree line) the better job at tracking the true number of infected people."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.014997,
     "end_time": "2020-04-10T00:18:57.351862",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.336865",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "> Tip: Click (Shift+ for multiple) on countries in the legend to filter the visualization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-04-10T00:18:57.396240Z",
     "iopub.status.busy": "2020-04-10T00:18:57.391242Z",
     "iopub.status.idle": "2020-04-10T00:18:57.641940Z",
     "shell.execute_reply": "2020-04-10T00:18:57.640587Z"
    },
    "papermill": {
     "duration": 0.274903,
     "end_time": "2020-04-10T00:18:57.642054",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.367151",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
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\"n_days\": 10, \"cases\": 18, \"infected\": 593.0, \"45_line\": 18}, {\"index\": 6351, \"location\": \"Iran\", \"date\": \"2020-02-22T00:00:00\", \"total_cases\": 28, \"total_infected\": 978.0, \"n_days\": 11, \"cases\": 28, \"infected\": 978.0, \"45_line\": 28}, {\"index\": 6352, \"location\": \"Iran\", \"date\": \"2020-02-23T00:00:00\", \"total_cases\": 43, \"total_infected\": 1501.0, \"n_days\": 12, \"cases\": 43, \"infected\": 1501.0, \"45_line\": 43}, {\"index\": 6353, \"location\": \"Iran\", \"date\": \"2020-02-24T00:00:00\", \"total_cases\": 61, \"total_infected\": 2336.0, \"n_days\": 13, \"cases\": 61, \"infected\": 2336.0, \"45_line\": 61}, {\"index\": 6354, \"location\": \"Iran\", \"date\": \"2020-02-25T00:00:00\", \"total_cases\": 95, \"total_infected\": 2922.0000000000005, \"n_days\": 14, \"cases\": 95, \"infected\": 2922.0000000000005, \"45_line\": 95}, {\"index\": 6355, \"location\": \"Iran\", \"date\": \"2020-02-26T00:00:00\", \"total_cases\": 139, \"total_infected\": 3513.0, \"n_days\": 15, \"cases\": 139, \"infected\": 3513.0, \"45_line\": 139}, {\"index\": 6356, \"location\": \"Iran\", \"date\": \"2020-02-27T00:00:00\", \"total_cases\": 245, \"total_infected\": 4747.0, \"n_days\": 16, \"cases\": 245, \"infected\": 4747.0, \"45_line\": 245}, {\"index\": 6357, \"location\": \"Iran\", \"date\": \"2020-02-28T00:00:00\", \"total_cases\": 388, \"total_infected\": 5823.0, \"n_days\": 17, \"cases\": 388, \"infected\": 5823.0, \"45_line\": 388}, {\"index\": 6358, \"location\": \"Iran\", \"date\": \"2020-02-29T00:00:00\", \"total_cases\": 593, \"total_infected\": 6566.0, \"n_days\": 18, \"cases\": 593, \"infected\": 6566.0, \"45_line\": 593}, {\"index\": 6359, \"location\": \"Iran\", \"date\": \"2020-03-01T00:00:00\", \"total_cases\": 978, \"total_infected\": 7161.000000000001, \"n_days\": 19, \"cases\": 978, \"infected\": 7161.000000000001, \"45_line\": 978}, {\"index\": 6360, \"location\": \"Iran\", \"date\": \"2020-03-02T00:00:00\", \"total_cases\": 1501, \"total_infected\": 8042.000000000001, \"n_days\": 20, \"cases\": 1501, \"infected\": 8042.000000000001, \"45_line\": 1501}, {\"index\": 6361, \"location\": \"Iran\", \"date\": \"2020-03-03T00:00:00\", \"total_cases\": 2336, \"total_infected\": 9000.0, \"n_days\": 21, \"cases\": 2336, \"infected\": 9000.0, \"45_line\": 2336}, {\"index\": 6362, \"location\": \"Iran\", \"date\": \"2020-03-04T00:00:00\", \"total_cases\": 2922, \"total_infected\": 10075.0, \"n_days\": 22, \"cases\": 2922, \"infected\": 10075.0, \"45_line\": 2922}, {\"index\": 6363, \"location\": \"Iran\", \"date\": \"2020-03-05T00:00:00\", \"total_cases\": 3513, \"total_infected\": 11364.0, \"n_days\": 23, \"cases\": 3513, \"infected\": 11364.0, \"45_line\": 3513}, {\"index\": 6364, \"location\": \"Iran\", \"date\": \"2020-03-06T00:00:00\", \"total_cases\": 4747, \"total_infected\": 12729.0, \"n_days\": 24, \"cases\": 4747, \"infected\": 12729.0, \"45_line\": 4747}, {\"index\": 6365, \"location\": \"Iran\", \"date\": \"2020-03-07T00:00:00\", \"total_cases\": 5823, \"total_infected\": 13938.0, \"n_days\": 25, \"cases\": 5823, \"infected\": 13938.0, \"45_line\": 5823}, {\"index\": 6366, \"location\": \"Iran\", \"date\": \"2020-03-08T00:00:00\", \"total_cases\": 6566, \"total_infected\": 14991.0, \"n_days\": 26, \"cases\": 6566, \"infected\": 14991.0, \"45_line\": 6566}, {\"index\": 6367, \"location\": \"Iran\", \"date\": \"2020-03-09T00:00:00\", \"total_cases\": 7161, \"total_infected\": 16169.0, \"n_days\": 27, \"cases\": 7161, \"infected\": 16169.0, \"45_line\": 7161}, {\"index\": 6368, \"location\": \"Iran\", \"date\": \"2020-03-10T00:00:00\", \"total_cases\": 8042, \"total_infected\": 17361.0, \"n_days\": 28, \"cases\": 8042, \"infected\": 17361.0, \"45_line\": 8042}, {\"index\": 6369, \"location\": \"Iran\", \"date\": \"2020-03-11T00:00:00\", \"total_cases\": 9000, \"total_infected\": 18407.0, \"n_days\": 29, \"cases\": 9000, \"infected\": 18407.0, \"45_line\": 9000}, {\"index\": 6370, \"location\": \"Iran\", \"date\": \"2020-03-12T00:00:00\", \"total_cases\": 10075, \"total_infected\": 19644.0, \"n_days\": 30, \"cases\": 10075, \"infected\": 19644.0, \"45_line\": 10075}, {\"index\": 6371, \"location\": \"Iran\", \"date\": \"2020-03-13T00:00:00\", \"total_cases\": 11364, \"total_infected\": 20610.0, \"n_days\": 31, \"cases\": 11364, \"infected\": 20610.0, \"45_line\": 11364}, {\"index\": 6372, \"location\": \"Iran\", \"date\": \"2020-03-14T00:00:00\", \"total_cases\": 12729, \"total_infected\": 21638.0, \"n_days\": 32, \"cases\": 12729, \"infected\": 21638.0, \"45_line\": 12729}, {\"index\": 6373, \"location\": \"Iran\", \"date\": \"2020-03-15T00:00:00\", \"total_cases\": 13938, \"total_infected\": 23049.0, \"n_days\": 33, \"cases\": 13938, \"infected\": 23049.0, \"45_line\": 13938}, {\"index\": 6374, \"location\": \"Iran\", \"date\": \"2020-03-16T00:00:00\", \"total_cases\": 14991, \"total_infected\": 24811.0, \"n_days\": 34, \"cases\": 14991, \"infected\": 24811.0, \"45_line\": 14991}, {\"index\": 6375, \"location\": \"Iran\", \"date\": \"2020-03-17T00:00:00\", \"total_cases\": 16169, \"total_infected\": 27017.0, \"n_days\": 35, \"cases\": 16169, \"infected\": 27017.0, \"45_line\": 16169}, {\"index\": 6376, \"location\": \"Iran\", \"date\": \"2020-03-18T00:00:00\", \"total_cases\": 17361, \"total_infected\": 29406.0, \"n_days\": 36, \"cases\": 17361, \"infected\": 29406.0, \"45_line\": 17361}, {\"index\": 6377, \"location\": \"Iran\", \"date\": \"2020-03-19T00:00:00\", \"total_cases\": 18407, \"total_infected\": 32331.999999999996, \"n_days\": 37, \"cases\": 18407, \"infected\": 32331.999999999996, \"45_line\": 18407}, {\"index\": 6378, \"location\": \"Iran\", \"date\": \"2020-03-20T00:00:00\", \"total_cases\": 19644, \"total_infected\": 35408.0, \"n_days\": 38, \"cases\": 19644, \"infected\": 35408.0, \"45_line\": 19644}, {\"index\": 6379, \"location\": \"Iran\", \"date\": \"2020-03-21T00:00:00\", \"total_cases\": 20610, \"total_infected\": 38309.0, \"n_days\": 39, \"cases\": 20610, \"infected\": 38309.0, \"45_line\": 20610}, {\"index\": 6380, \"location\": \"Iran\", \"date\": \"2020-03-22T00:00:00\", \"total_cases\": 21638, \"total_infected\": 41495.0, \"n_days\": 40, \"cases\": 21638, \"infected\": 41495.0, \"45_line\": 21638}, {\"index\": 6381, \"location\": \"Iran\", \"date\": \"2020-03-23T00:00:00\", \"total_cases\": 23049, \"total_infected\": 44604.99999999999, \"n_days\": 41, \"cases\": 23049, \"infected\": 44604.99999999999, \"45_line\": 23049}, {\"index\": 6382, \"location\": \"Iran\", \"date\": \"2020-03-24T00:00:00\", \"total_cases\": 24811, \"total_infected\": 47593.0, \"n_days\": 42, \"cases\": 24811, \"infected\": 47593.0, \"45_line\": 24811}, {\"index\": 6383, \"location\": \"Iran\", \"date\": \"2020-03-25T00:00:00\", \"total_cases\": 27017, \"total_infected\": 50467.99999999999, \"n_days\": 43, \"cases\": 27017, \"infected\": 50467.99999999999, \"45_line\": 27017}, {\"index\": 6384, \"location\": \"Iran\", \"date\": \"2020-03-26T00:00:00\", \"total_cases\": 29406, \"total_infected\": 53183.0, \"n_days\": 44, \"cases\": 29406, \"infected\": 53183.0, \"45_line\": 29406}, {\"index\": 6385, \"location\": \"Iran\", \"date\": \"2020-03-27T00:00:00\", \"total_cases\": 32332, \"total_infected\": 55743.0, \"n_days\": 45, \"cases\": 32332, \"infected\": 55743.0, \"45_line\": 32332}, {\"index\": 6386, \"location\": \"Iran\", \"date\": \"2020-03-28T00:00:00\", \"total_cases\": 35408, \"total_infected\": 58226.0, \"n_days\": 46, \"cases\": 35408, \"infected\": 58226.0, \"45_line\": 35408}, {\"index\": 6387, \"location\": \"Iran\", \"date\": \"2020-03-29T00:00:00\", \"total_cases\": 38309, \"total_infected\": 60500.0, \"n_days\": 47, \"cases\": 38309, \"infected\": 60500.0, \"45_line\": 38309}, {\"index\": 6388, \"location\": \"Iran\", \"date\": \"2020-03-30T00:00:00\", \"total_cases\": 41495, \"total_infected\": 62589.0, \"n_days\": 48, \"cases\": 41495, \"infected\": 62589.0, \"45_line\": 41495}, {\"index\": 6389, \"location\": \"Iran\", \"date\": \"2020-03-31T00:00:00\", \"total_cases\": 44605, \"total_infected\": 64586.0, \"n_days\": 49, \"cases\": 44605, \"infected\": 64586.0, \"45_line\": 44605}, {\"index\": 6390, \"location\": \"Iran\", \"date\": \"2020-04-01T00:00:00\", \"total_cases\": 47593, \"total_infected\": 66220.0, \"n_days\": 50, \"cases\": 47593, \"infected\": 66220.0, \"45_line\": 47593}, {\"index\": 6391, \"location\": \"Iran\", \"date\": \"2020-04-02T00:00:00\", \"total_cases\": 50468, \"total_infected\": 68349.80971855647, \"n_days\": 51, \"cases\": 50468, \"infected\": 68349.80971855647, \"45_line\": 50468}, {\"index\": 6392, \"location\": \"Iran\", \"date\": \"2020-04-03T00:00:00\", \"total_cases\": 53183, \"total_infected\": 70548.11973063843, \"n_days\": 52, \"cases\": 53183, \"infected\": 70548.11973063843, \"45_line\": 53183}, {\"index\": 6393, \"location\": \"Iran\", \"date\": \"2020-04-04T00:00:00\", \"total_cases\": 55743, \"total_infected\": 72817.13318621377, \"n_days\": 53, \"cases\": 55743, \"infected\": 72817.13318621377, \"45_line\": 55743}, {\"index\": 6394, \"location\": \"Iran\", \"date\": \"2020-04-05T00:00:00\", \"total_cases\": 58226, \"total_infected\": 75159.12409435963, \"n_days\": 54, \"cases\": 58226, \"infected\": 75159.12409435963, \"45_line\": 58226}, {\"index\": 6395, \"location\": \"Iran\", \"date\": \"2020-04-06T00:00:00\", \"total_cases\": 60500, \"total_infected\": 77576.43960227807, \"n_days\": 55, \"cases\": 60500, \"infected\": 77576.43960227807, \"45_line\": 60500}, {\"index\": 6396, \"location\": \"Iran\", \"date\": \"2020-04-07T00:00:00\", \"total_cases\": 62589, \"total_infected\": 80071.50234761092, \"n_days\": 56, \"cases\": 62589, \"infected\": 80071.50234761092, \"45_line\": 62589}, {\"index\": 6397, \"location\": \"Iran\", \"date\": \"2020-04-08T00:00:00\", \"total_cases\": 64586, \"total_infected\": 82646.81288641127, \"n_days\": 57, \"cases\": 64586, \"infected\": 82646.81288641127, \"45_line\": 64586}, {\"index\": 6398, \"location\": \"Iran\", \"date\": \"2020-04-09T00:00:00\", \"total_cases\": 66220, \"total_infected\": 85304.95219920494, \"n_days\": 58, \"cases\": 66220, \"infected\": 85304.95219920494, \"45_line\": 66220}]}}, {\"mode\": \"vega-lite\"});\n",
       "</script>"
      ],
      "text/plain": [
       "alt.LayerChart(...)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hide_input\n",
    "# Plot it using Altair\n",
    "data_pc = data_final[['location', 'date', 'total_cases', 'total_infected']].copy()\n",
    "\n",
    "countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
    "             \"Portugal\", \"United States\", \"Singapore\",\"South Korea\", \"Japan\", \n",
    "             \"Brazil\",\"Iran\"]\n",
    "data_countries = []\n",
    "data_countries_pc = []\n",
    "\n",
    "for i in countries:\n",
    "    data_pc.loc[data_pc.location == i,\"total_infected\"] = data_pc.loc[data_pc.location == i,\"total_infected\"]\n",
    "    data_pc.loc[data_pc.location == i,\"total_cases\"] = data_pc.loc[data_pc.location == i,\"total_cases\"]\n",
    "    # get each country time series\n",
    "filter1 = data_pc[\"total_infected\"] > 1\n",
    "for i in countries:\n",
    "    filter_country = data_pc[\"location\"]== i\n",
    "    data_countries_pc.append(data_pc[filter_country & filter1])\n",
    "\n",
    "\n",
    "plot(data_countries_pc, \"scatter\", True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.017294,
     "end_time": "2020-04-10T00:18:57.676809",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.659515",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Latest Observed vs. Estimate of Infected Cases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2020-04-10T00:18:57.737288Z",
     "iopub.status.busy": "2020-04-10T00:18:57.736699Z",
     "iopub.status.idle": "2020-04-10T00:18:57.741605Z",
     "shell.execute_reply": "2020-04-10T00:18:57.742328Z"
    },
    "papermill": {
     "duration": 0.048983,
     "end_time": "2020-04-10T00:18:57.742514",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.693531",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Observed Cases</th>\n",
       "      <th>Estimated Infected</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Country</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Brazil</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>18,092</td>\n",
       "      <td>45,263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>China</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>82,883</td>\n",
       "      <td>83,448</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>France</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>118,781</td>\n",
       "      <td>188,038</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Germany</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>118,181</td>\n",
       "      <td>163,557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iran</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>66,220</td>\n",
       "      <td>85,305</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Italy</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>143,626</td>\n",
       "      <td>177,677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Japan</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>4,667</td>\n",
       "      <td>9,943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Portugal</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>13,956</td>\n",
       "      <td>21,138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Singapore</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>1,910</td>\n",
       "      <td>3,932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Korea</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>10,423</td>\n",
       "      <td>10,804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Spain</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>153,222</td>\n",
       "      <td>206,399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United Kingdom</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>65,872</td>\n",
       "      <td>119,124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>United States</th>\n",
       "      <td>2020-04-09</td>\n",
       "      <td>461,437</td>\n",
       "      <td>844,721</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Date Observed Cases Estimated Infected\n",
       "Country                                                    \n",
       "Brazil         2020-04-09         18,092             45,263\n",
       "China          2020-04-09         82,883             83,448\n",
       "France         2020-04-09        118,781            188,038\n",
       "Germany        2020-04-09        118,181            163,557\n",
       "Iran           2020-04-09         66,220             85,305\n",
       "Italy          2020-04-09        143,626            177,677\n",
       "Japan          2020-04-09          4,667              9,943\n",
       "Portugal       2020-04-09         13,956             21,138\n",
       "Singapore      2020-04-09          1,910              3,932\n",
       "South Korea    2020-04-09         10,423             10,804\n",
       "Spain          2020-04-09        153,222            206,399\n",
       "United Kingdom 2020-04-09         65,872            119,124\n",
       "United States  2020-04-09        461,437            844,721"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hide_input\n",
    "label1 = 'Observed Cases'\n",
    "label2 = 'Estimated Infected'\n",
    "temp = pd.concat([x.copy() for x in data_countries_pc]).loc[lambda x: x.date >= '3/1/2020']\n",
    "\n",
    "metric_name1 = f'{label1}'\n",
    "metric_name2 = f'{label2}'\n",
    "temp.columns = ['Country', 'Date', metric_name1, metric_name2]\n",
    "# temp.loc[:, 'month'] = temp.date.dt.strftime('%Y-%m')\n",
    "temp.loc[:, \"Observed Cases\"] = temp.loc[:, \"Observed Cases\"].round(0).map('{:,.0f}'.format)\n",
    "temp.loc[:, \"Estimated Infected\"] = temp.loc[:, \"Estimated Infected\"].round(0).map('{:,.0f}'.format)\n",
    "temp.groupby('Country').last()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.01785,
     "end_time": "2020-04-10T00:18:57.778412",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.760562",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Methodology"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.016557,
     "end_time": "2020-04-10T00:18:57.812106",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.795549",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We argue that the number of infected in the past can be inferred using today's number of deaths and average fatality rate from confirmed cases in the following way:\n",
    "\n",
    "{%raw%}$$I_{t-j} = \\frac{D_t}{{CFR}_t}$${%endraw%}\n",
    "\n",
    "where {% raw %}$I_t${% endraw %} = number of infected, {% raw %}$D_t${% endraw %} = number of deaths, and {% raw %}${CFR}_t ${% endraw %} = case fatality rate = {% raw %}$\\frac{D}{C}${% endraw %}. The {% raw %}$j${% endraw %} depends on the average number of days that covid patients die after having the first symptoms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "papermill": {
     "duration": 0.017494,
     "end_time": "2020-04-10T00:18:57.847000",
     "exception": false,
     "start_time": "2020-04-10T00:18:57.829506",
     "status": "completed"
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   "source": [
    "**Assumption 1**: The case fatality rate is a good proxy for the fatality rate of the infected population\n"
   ]
  },
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   "source": [
    "Then, in order to estimate the current number of infected {% raw %}$I_t${% endraw %} we need to estimate its growth rate from {% raw %}$t-j${% endraw %} to {% raw %}$t${% endraw %}.\n",
    "\n",
    "{% raw %}$$I_t = (1+\\hat{g})^j I_{t-j}$${% endraw %}"
   ]
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   "source": [
    "**Assumption 2**: The growth rate of infected $\\hat{g}$ is an unbiased estimate of $g$ .\n",
    "\n",
    "For now we estimate $g$ using the average growth rate since having the first infected person."
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   "source": [
    "**Assumption 3**: It takes on average 8 days to die after having the first symptoms."
   ]
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   "source": [
    "This analysis was conducted by [Joao B. Duarte](http://jbduarte.com). Relevant sources are listed below: \n",
    "\n",
    "\n",
    "1. [2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository by Johns Hopkins CSSE](https://systems.jhu.edu/research/public-health/ncov/) [GitHub repository](https://github.com/CSSEGISandData/COVID-19). \n",
    "\n",
    "2. [Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), \"The Next Generation of the Penn World Table\" American Economic Review, 105(10), 3150-3182](https://www.rug.nl/ggdc/productivity/pwt/related-research)\n"
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